Steering opinion dynamics via containment control

Abstract

In this paper, we model the problem of influencing the opinions of groups of individuals as a containment control problem, as in many practical scenarios, the control goal is not full consensus among all the individual opinions, but rather their containment in a certain range, determined by a set of leaders. As in classical bounded confidence models, we consider individuals affected by the confirmation bias, thus tending to influence and to be influenced only if their opinions are sufficiently close. However, here we assume that the confidence level, modeled as a proximity threshold, is not constant and uniform across the individuals, as it depends on their opinions. Specifically, in an extremist society, the most radical agents (i.e., those with the most extreme opinions) have a higher appeal and are capable of influencing nodes with very diverse opinions. The opposite happens in a moderate society, where the more connected (i.e., influential) nodes are those with an average opinion. In three artificial societies, characterized by different levels of extremism, we test through extensive simulations the effectiveness of three alternative containment strategies, where leaders have to select the set of followers they try to directly influence. We found that, when the network size is small, a stochastic time-varying pinning strategy that does not rely on information on the network topology proves to be more effective than static strategies where this information is leveraged, while the opposite happens for large networks where the relevance of the topological information is prevalent.

Opinion Dynamics Steering using Stochastic Search

“…Since then, a variety of both theoretical and application-oriented models have been proposed [9], [10], [11], [12], [13]. However, despite the abundance of literature on the modeling side, research on opinion dynamics control remains limited and mainly focuses on pinning control for deterministic opinion dynamics models [14], [15], [16]. Pinning control establishes a virtual leader that can influence the agents in a network.…”

Partial containment control over signed graphs

“…Motivated by that, Ji and coworkers introduced the socalled containment control problem, where multiple leaders have to drive a group of mobile agents within a desired convex polytope [5]. Later works have further analyzed this problem to account for the presence of directed interactions [6], possible switches in the network topology [7], [8], uncertainty [9], and higher-order dynamics [10], [11]. As noted by Altafini in [12], most of the works on consensus and containment control relies on the assumption of cooperation among the agents in the system, as all the network edges are assumed to have positive weights.…”

Influence Dynamics and Consensus in an Opinion-Neighborhood based Modified Vicsek-like Social Network

“…[24]- [26], classify agents as closed, open and moderate, and analyse different group compositions. [27]- [32] classify agents based on opinions, and discuss the effect of contrarians, extremists and forceful agents. [33] analyses the impact of well-informed minorities in the midst of an uninformed majority.…”

“…In the context of complex systems, [32], [48], [49] explore a dynamic member-set, network based on proximity rule, and edge snapping, respectively. Instead, here, a network derived from individual opinions, thresholds and interactions evolve in accordance with prescribed rules, reflecting dynamic interpersonal relationships.…”